TY - BOOK

T1 - Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

AU - Sarmany, D.

AU - Izsak, F.

AU - van der Vegt, Jacobus J.W.

PY - 2010/1

Y1 - 2010/1

N2 - We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.

AB - We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.

KW - METIS-270717

KW - Numerical mathematics

KW - EWI-17325

KW - Electromagnetic waves

KW - MSC-00A72

KW - Scientific computation

KW - Finite Element Method

KW - IR-69763

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -